2020arXiv (Cornell University)Open access

Pfaffian control of some polynomials involving the $j$--function and Weierstrass elliptic functions

J. V. Armitage

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Abstract

We give new bounds on the zeros of polynomials in $z$ and the $j$--function, and $z$ and Weierstrass elliptic functions with rectangular associated lattice, controlling the zeros of these functions by their tame behaviour on the boundaries of their respective fundamental domains.

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We give new bounds on the zeros of polynomials in $z$ and the $j$--function, and $z$ and Weierstrass elliptic functions with rectangular associated lattice, controlling the zeros of these functions by their tame behaviour on the boundaries of their respective fundamental domains.

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Available abstract

We give new bounds on the zeros of polynomials in $z$ and the $j$--function, and $z$ and Weierstrass elliptic functions with rectangular associated lattice, controlling the zeros of these functions by their tame behaviour on the boundaries of their respective fundamental domains.

Key concepts: Pfaffian, Weierstrass functions, Elliptic function, Mathematics, Pure mathematics, Algebra over a field, Function (biology), Mathematical analysis

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